What do your arguments (conf or bat) look like? It seems the 7870's use -g 2 and 7850's use -g 1; I had problems trying to mix cards like this with 7950 and 7970. At the very least, use all -g 1 for them.
Based on the thread below, my bat for those cards might look like.
https://litecoin.info/Mining_hardware_comparison-o pooladdress -u username.1 -p pass --scrypt -w 256,256,256,256 -g 1 --thread-concurrency 8192,8192,8192,10240 --intensity 19,19,19,19 --auto-fan --auto-gpu
You can also start with as few arguments as possible, then add them until it doesn't run, then go back to the last usable settings.
Delete your .bin's in the cgminer folder first, then try the barebones bat, then check to see what the .bin it created is called. Example: scrypt130511Caymanglg2tc
7168w256l4.bin, so this card's basic thread concurrency is 7168.
-o pooladdress -u username.1 -p pass --scrypt --intensity 17,17,17,17
Also, I recommend
Catalyst 13.1
SDK 2.7
cgminer 3.3.1
Good luck and let me know how it goes!
Edit: I thought you were new and wrote it like that, so I hope there's something here for you