My understanding is that a multi-wire branch circuit requires a little more than just what the OP said. For example, the 2 hot wires should have a voltage between them. There is also more detail to ensure the neutral doesn't become overloaded. I think someone should add in more detail here before someone burns up a TV or worse - a house.
That's redundant. If the 2 hot wires show voltage (240v) between them, there is no overloading the neutral, it will only see the difference in the neutral current.
The problem is when each wire has voltage but there is no voltage between them. That is when you get the sum of currents on the neutral, which can overload it.
I think Jim put the proper name on it and I assumed a properly wired MWBC. The question is why can't he use it? We have been chasing the AFCI question. In re-reading the OP's question, he never said it was for the kitchen. He said "like running .... For the kitchen". So we need to ask is this really for the kitchen, or is it a circuit for some other use or another location ?