A time-invariant (constant channel gains) K-user interference channel is considered, where all interference (cross) channel gains are integers. For such channels, previous results demonstrate that the number of degrees of freedom is very sensitive to slight variations in the direct channel gains. In this paper we derive an achievable rate region for such channels which is valid for finite SNR. At moderate values of SNR the derived rate region is robust to slight variations in the direct channel gains. At asymptotic high SNR conditions, the known results on the degrees of freedom are recovered. The new rate region is based on lattice interference alignment. The result is established via a new coding theorem for the two-user Gaussian multiple-access channel where both users use a single linear code.