I don't have any advice, but I wanted to say I'm glad you asked this question. I'm making a quilt for my daughter, and the whole reason I started was because I wanted to be able to use some of her baby clothes to make it. I'd wondered the same thing about mixing the stretchy cotton knits from her clothes with the plainer woven fabrics that I see in the shops.
Please let me know how the interfacing thing works out. I'll know in about three weeks exactly how much baby clothing I can use (that's when I find out whether I'll be having another girl to use hand-me-downs), so until then I'm piecing with fabric I've bought.