As a former kid, let me break it down to you. Step mom or dad sounds evil thanks to fairy tales. So, I called my Other Mom, Mom. My Mommy didn't have a problem with it because we are very close and she knows she gave birth to me. And my parents got along so there was no real issue.

Talk to the Dad and let him know that it's not your preference, but you love his kids just like they were yours. You aren't trying to replace him because you know you couldn't, but you are in their lives and if they should call you dad, you won't correct them.