SLI needs to be with the same card. Crossfire needs to be with the same hundreds: 58XX or 57XX (ie 5750 with 5770). 58XX with 57XX will not be possible in crossfire.
Why would you want them to run independelty? You can have them dedicated to a single task or more, with both of them working together... But yes, most games/applications and such have options to choose what card(s) you want to use. Without them working together, they will be no problem to work with both a 5770 and a 5870 (Though know that you will never be able to crossfire).