That's strange. AHCI is a subset of RAID. So as long as your SSD is not part of the RAID array it automatically defaults to AHCI mode and should be recognized.
1.) Connect your SSD to one of the Intel 6Gb/s ports (SATA1 or SATA2) in AHCI mode.
2.) Connect your 2 HDDs to the ASMedia 6Gb/s ports (SATA7 & SATA8) in RAID mode.
3.) Reboot into the ASMedia's RAID BIOS and create a new array.