Superposition coding with successive cancellation decoding for interference channels is investigated as a low-complexity alternative to the rate-optimal simultaneous decoding. It is shown that regardless of the number of superposition layers and the code distribution of each layer, the standard rate-splitting scheme by Grant, Rimoldi, Urbanke, and Whiting for multiple access channels fails to achieve the simultaneous decoding inner bound on the capacity region for interference channels. A new coding scheme is proposed that uses coding over multiple blocks and sliding-window decoding. With at most two superposition layers, this scheme achieves the simultaneous decoding inner bound for any two-user-pair interference channels without using high-complexity simultaneous multiuser sequence detection. The proposed coding scheme can be also extended to achieve the performance of simultaneous decoding for general interference networks, including the Han-Kobayashi inner bound.