A few weeks before we got engaged my MIL asked me to call her mum. It was strange at first but now it seems natural. I also call my FIL by the families cultural name for dad.
After we got married my husband began calling my parents "Mum" and "Bloke" (a nickname my brother calls my dad). I remember the first time my husband called my mum "mum" she got a little teary. It was sweet
, and she commented to me how nice it was to have my husband call her that.
My brother also introduces my husband to people as his brother, as they get along really well. However being clearly from two different cultural backgrounds it confuses people a lot if I'm not there with them.
My husband and I are extremely lucky though as our families getting along extremely well, our photographer made a comment to someone at our wedding as it didn't seem like two families but one big family.