In this paper, we investigate physical-layer security for a heterogeneous cellular network consisting of a macro cell and a small cell in the presence of a passive eavesdropper that intends to tap both the macro-cell and small-cell transmissions. Both the orthogonal spectrum sharing (OSS) and non-orthogonal spectrum sharing (NOSS) are considered for the heterogeneous cellular network. The OSS allows the macro cell and small cell to access a given spectrum band in an orthogonal manner, whereas the NOSS enables them to access the same spectrum simultaneously and mutual interference exits. As a consequence, we present two NOSS schemes, namely the interference-limited NOSS (IL-NOSS) and interference-canceled NOSS (IC-NOSS), where the mutual interference is constrained below a tolerable level in the IL-NOSS through power control and the IC-NOSS scheme exploits a specially-designed signal for canceling out the interference received a legitimate cellular user while confusing the passive eavesdropper. We derive closed-form expressions for an overall secrecy outage probability of the OSS, IL-NOSS, and IC-NOSS schemes, which take into account the transmission secrecy of both the macro cell and small cell. We further characterize the secrecy diversity of OSS, IL-NOSS and IC-NOSS schemes through an asymptotic secrecy outage analysis in the high signal-to-noise ratio region. It is shown that the OSS and IL-NOSS methods obtain the same secrecy diversity gain of zero only, and a higher secrecy diversity gain of one is achieved by the IC-NOSS scheme. Additionally, numerical results demonstrate that the IC-NOSS scheme significantly performs better than the OSS and IL-NOSS methods in terms of the overall secrecy outage probability.