The objective of this paper is to propose a loss compensated DC optimal power flow (OPF) framework for an integrated AC and multi-terminal high voltage direct current system. The proposed DCOPF framework is established on the line flow based formulation. The losses in both AC and HVDC transmission lines are represented as a piecewise linear function of the terminal-averaged power flows. Piecewise linear representation, eventually, transforms the nonlinear constraints into linear constraints in the OPF formulation. This in effect reduces the computational complexities of the OPF calculation. In addition to uncontrolled AC transmission lines, controlled AC transmission lines are also considered. Appropriate case studies are carried out on a modified IEEE 30-bus and a modified IEEE 118-bus systems to demonstrate the accuracy and efficiency of the proposed DCOPF framework. © 2017 IEEE.