Of course you can!
I do it all the time as anyone who has glanced at any of my quilts (or indeed read any of my posts) can tell you.
I was in The Emporia once, showing off some creation or the other, and a peeps came over with a horrified look on her face.... 'Is that batik?' she asked incredulously ... 'yup' I said, 'Why?' and she told me, in all seriousness, that she was told you couldn't mix cotton and batik in the same quilt ????
Why not????