How do you backup two hard drives using one external hard drive?

Use the "System Backup" Option and select the drives that you want backed up. I use Windows Backup, as well as EaseUS Todo Backup.

I prefer SyncBack, it has tons of options for manual and scheduled backups and you can specify subdirectories and folder/file rules for source and destination.

As USAFRet suggested you should do a folder per drive.

If you want to copy your user folder with your documents in it on your OS drive this fine but if you want to copy your programs and OS then you need to do a disk image. You can use a program called macrium reflect for that which is also free and will allow you to setup schedules.
The only one con to this software is that you either manually have to delete the old images or have a batch file script do it.

And FYI don't use windows backup, it is so unintuitive compared to syncback and takes up significantly more space then any other disk imaging software I have used.

A question re SyncBack...

The program obviously has the capability of backing up files/folders from the user's boot drive that contains the OS. Assuming that drive becomes defective or corrupted so that it's unbootable/dysfunctional, can the SyncBack program easily restore the system to a bootable, functional state? Is some sort of recovery-type process necessary to accomplish this?

No, it isn't a boot capable backup, only files and folders. But for what it is, it works quite well.
For instance, from one of my secondary drives, I don't need the whole thing imaged. Just a few folders copied elsewhere on a schedule.

From Any Drive/Folder A, to Any Drive/Folder B.

I've been doing this another way, not quite as the tool was intended, but for a reason. I wanted to be sure that, if my C: drive failed, I could replace it quickly with a complete backup that I could boot from and get running again. There also is a D: drive for additional data only (not bootable).

My external unit is a Seagate drive mounted in an Azio enclosure, and connected via eSATA. So I downloaded the Seagate utility Disk Wizard which appears to be a customized version of Acronis True Image. It includes a tool for drive cloning, which is what I use for this. But it is designed to make a clone TO only a Seagate HDD, so that's why I use it.

First, I use the utility to Delete any and all previous Partitions on the external drive. Then I clone my C: drive to the external unit. BUT I do NOT just accept its default settings. I use the menus to make the clone copy smaller than the original C: drive, but large enough to accept all its contents, and bootable. THEN I do a separate clone of the D: drive to that same external unit, doing a similar size adjustment, and putting that second clone image into the Unallocated Space left over from the first cloning operation. That clone does not need to be bootable. Now that external unit has TWO clone copies on it - one for each of my internal drives.

If I then look in My Computer, the C: and D: drives are there of course, plus identical versions of them under different letter names on the external unit. And all are accessible.

Now came the critical test. I disconnected my two internal HDD's. Then I removed the HDD unit from the external enclosure, mounted it inside my case and connected it up. I made sure that I connected its data cable to the SAME mobo SATA port as my original C: drive was on, just so the BIOS would have no difficulty finding the boot device. I powered on and sure enough, the machine booted from the first Partition of the (formerly external) HDD, and I had both C: and D: drives to work with containing all my data. Only difference was, the two drives each were a bit smaller than the originals.

Having proved it worked, I removed the "external" unit and re-mounted it in my enclosure, then reconnected my original two internal HDD's. Of course, the machine was back to normal, and I had my backups in the two Partitions of the external HDD unit.

I can wipe the HDD unit in the external enclosure any time ad re-make the two clones. And of course I keep it disconnected from the computer while not using it.

The major differences between what I do and a normal backup system are: (a) I don't make any incremental backups - only complete backups; and, (b) my backups are not in any proprietary file - they are just complete clones of my original drives, and I can use the HDD containing the clones to replace my original drives completely (allowing for size differences) so I can boot and run normally after a relatively simple hardware drive transplant, rather than a Restore operation using software. There's also the small factor that, for a short period of time while I delete all previous stuff on the external and re-make the two clones, I have no backups at all.

Re: your backup query - you might want to consider a simpler & more comprehensive approach along the following lines...

Why not utilize a disk-cloning program on a routine basis to create bit-for-bit precise copies of your source drives - the 256 GB SSD (presumably your boot drive) & your secondary 2 TB HDD? What better backup system can one create than having at hand exact copies of their day-to-day working drives? So that in the event of a defective or corrupted drive and/or an unbootable system, the user can virtually immediately return his/her system to a bootable, totally functional system.

You can readily achieve that goal through the use of an appropriate disk-cloning program. (My comments are based on the program I use - Casper.)

In your situation you would multi-partition your 1.5 TB USBEHD into two partitions - one 256 GB (obviously to accommodate your boot drive) and a second partition of the remaining disk-space to accommodate your secondary 2 TB HDD. (I'm assuming, of course, that the latter partition would be of sufficient size to contain the total DATA CONTENTS of your 2 TB HDD).

By undertaking the disk-cloning operation for your two source drives on a reasonably frequent basis - say, weekly - the entire operation would probably take you about 3 to 4 minutes. Should you undertake the disk-cloning process more frequently, say two or three times a week it would probably take you about 2 minutes or so. The Casper program also has the capability of scheduling disk-cloning operations at predetermined times should that suit you.

The beauty of this backup approach is that it's reasonably quick to achieve and you gain the peace-of-mind knowing that if worse comes to worse because of a dysfunctional system you have at hand a precise copy of your once functional system with all data immediately accessible and without the need for any "recovery" type process. And as an added bonus - your USBEHD will be a bootable device. I repeat, what can be better?