If you don't have backups, there is little that you can do all by yourself. There are companies which specialize in resurrecting data from dead disk drives. Depending on how valuable the data was, you could send the drives to one of those companies and have them help you.

You have learned something important: Striping a pair of disk drives does not increase their reliability. In fact, it doubles your chances for a failure, because striping is not redundant.

I once striped a set of three disk drives so that I could get the speed improvements and the convenience of having a single large volume. I found that the speed improvement was miniscule, but I was stupid and simply left the striped set in place, thinking the convenience of the single large volume was worth it. I was wrong, because I lost one of the disk drives, too, and lost the entire array because of it. Fortunately I had plenty of backups, but some people aren't so lucky.

Going to a genuinely-redundant RAID1 or RAID5 configuration, instead of just striping, will prevent the problem in the future (as you have already surmised), but for now there is little you can do to recover the data unless you pay a professional to do the recovery.