If you send the binary file as a base64 encoded string, then you can post ot together with the other datafields.
{
"Name":"test.doc",
"BinaryFile":"ZmhhcGh2cGF3aGZwYWhuZ...etc...zI0MDc4NDY1NiB5dGhvaGF3"
}
And sending it as formdata? Does that work?