We introduce the interference-multiple-access channel, which is a discrete memoryless channel with two transmitters and two receivers, similar to the interference channel. One receiver is required to decode the information encoded at one transmitter, the other receiver is required to decode the messages from both transmitters. We provide an inner bound on the capacity region of this channel, as well as an outer bound for a special class of such channels. For this class, we also quantify the gap between inner and outer bound and show that the bounds match for a semi-deterministic channel, providing a complete characterization. For the Gaussian case, we show that the gap is at most 1 bit, yielding an approximate characterization.