We consider Device-to-Device (D2D)-enabled mobile edge computing offloading scenario, where a device can partially offload its computation task to the edge server or exploit the computation resources of proximal devices. Keeping in view the millisecond-scale latency requirement in 5G service scenarios and the spectrum scarcity, we focus on minimizing the sum of task execution latency of all the devices in a shared spectrum with interference. In particular, we provide an integrated framework for partial offloading and interference management using orthogonal frequency-division multiple access (OFDMA) scheme. Accordingly, we formulate total latency minimization as a mixed integer nonlinear programming (MINLP) problem by considering desired energy consumption, partial offloading, and resource allocation constraints. We use decomposition approach to solve our problem and propose a novel scheme named Joint Partial Offloading and Resource Allocation (JPORA). With aim to reduce the task execution latency, JPORA iteratively adjusts data segmentation and solves the underlying problem of quality of service (QoS)-aware communication resource allocation to the cellular links, and interference-aware communication resource allocation to D2D links. Extensive evaluation results demonstrate that JPORA achieves the lowest latency as compared to the other baseline schemes, meanwhile limiting the local energy consumption of user devices.