If it has a "coarse" feel, as bearisgray says, I wouldn't use it on the back as it sounds like it might be too stiff for a baby quilt which I like to be soft. I often use flannel for the back for newborns. Anyway, you would soften that feel by cutting the butterflies out and appliqueing them, but remember that some fusibles make things a bit stiff, too. So get the softest "hand" you can when appliqueing. It would be very pretty!