In this paper, we propose a novel framework, integer-forcing interference alignment, that can simultaneously exploit both signal-space and signal-scale alignment. We consider receivers that can decode integer-linear combinations of desired and interfering streams and then solve for their desired symbols. This is possible by using appropriate lattice codes at the transmitters and can be applied to the class of wireless communication systems that use linear beamforming. At the core of our architecture lies the compute-and-forward framework, which we extend here to encompass asymmetric power allocations. We evaluate the performance of our scheme in the context of the three-user interference channel through simulation results.