This paper examines the target detection problem in a multistatic passive radar with one noncooperative illuminator of opportunity (IO) and multiple distributed receivers. Specifically, we consider how to address the direct-path interference (DPI), which refers to the direct transmission from the IO to a receiver, to enhance passive detection performance. The DPI is in general much stronger (by many tens to even over a hundred dB) than the target echo. It is standard for a passive radar to apply some kind of interference cancellation by using, e.g., an adaptive array, to reduce the DPI. However, due to practical limitations of such techniques and the significant difference in strength between the DPI and target signal, the residual DPI after cancellation is often at a nonnegligible level. Unlike most existing passive detectors which ignore such residual DPI, we consider explicitly its effect and develop two new detectors under the conditions when the noise level is known and, respectively, when it is unknown. Another distinction from existing solutions is that the proposed detectors exploit the correlation of the IO waveform for passive detection. The proposed detectors are developed within the generalized likelihood ratio test (GLRT) framework, which involves nonlinear estimation that is solved using the expectation-maximization algorithm. Numerical results are presented to illustrate the performance of the proposed methods and several well-known passive detectors.