The performance of heterogeneous networks (HetNets) is investigated with both direct and relay-aided transmission strategies in a macrocell. We first propose an interference cancelation scheme at the macro base station on the basis of canceling cross-tier interferences from the macro base station to small-cell users. Then, expressions of the probability density function (PDF) and cumulative distribution function (CDF) of all receivers in both macro and small cells are derived, and the closed-form overall outage probability, average bit error rate (BER), and spectral efficiency of the network are obtained. Based on the derivations, we propose two adaptive relay-aided transmission schemes with instantaneous and statistical channel state information (CSI) to further improve the spectral efficiency. We show that the SNR boost at the small-cell mobile station comes from the cancelation of the cross-layer interference by the macro base station. Therefore, the performance of the small cell is improved greatly with interference cancelation, while the overall performance of the HetNet is also ameliorated. The numerical results finally show the validity of our analysis.