A new type of dual-channel interference microscope for quantitative phase imaging of transparent microscopic object is presented in this paper, which is comprised of an ordinary unpolarized cube beam-splitter and a ready-made Fresnel bi-prism. For this proposed microscope, the cube beam-splitter is tilted in an unconventional way, and the incident beam is only incident to one half of the cube beam-splitter and it is parallel with the central semi-reflecting layer of the cube beam-splitter. Subsequently, two copies of incident beam are created, the transmission beam is the simply replica and the reflection beam is the mirror-reverted replica. Behind the cube beam-splitter, the Fresnel bi-prism is placed in alignment with the cube beam-splitter and used to deflect the two generated beams to encounter and form the off-axis interference. Based on this kind of off-axis interference mode, we only need to record one interferogram for phase retrieval. Using this method, when the sample is only irradiated by one half of the incident beam, we can only use a single digital camera to record two symmetrical interference channels with a relative π (rad) phase-shift in one interferogram simultaneously. In addition, because of using less ordinary off-the-shelf optical elements, our method is simple and easy to operate with low cost, and it may be applied to traditional inverted optical microscope. Experimental results show that this method is suitable for quantitative phase imaging of transparent microscopic object.