what type of cat is this

The cat in this picture is most definitely not a Birman.
And....Birmans are not a mix of Siamese with Persian. See here for a CFA breed explanation. http://www.cfa.org
I know the Birman breed well. I have one - CFA papers and all...... and I have relatives who have had Birman's in the past that were registered as well.

It is a birman, a breed obtained by mixing siamese cats and persian. I have one myself! her name is Phoebe. Sorry I cannot upload a picture right now, but visit my page! Her name is Phoebe

definitely a siamese mix

He's a beautiful cat, however.....
Mixed-breed cats, unlike dogs, are generally not categorized to specific breeds. If you don't know the lineage of your cat (ie. you don't know his parents and/or he's more than one generation removed from a pure-bred) then he's simply a domestic medium hair cat with linx-point, mitted markings. All sorts of markings occur naturally in domestic cats but it doesn't mean the cat is related to a specific breed. My cat, Chloe is a great example.... she could pass for a torti-point, mitted ragdoll, but she's not at all. She's simply a domestic, medium hair cat with torti-point, mitted markings.

Oh, I forgot Himalaya - might have some Himalaya, too.