This paper develops a cross layer model for both interference and coexistence analysis of a multi-Gbps millimeter-wave wireless personal area network (WPAN) system with directional antennas. The model takes into consideration realistic 60GHz propagation channel and high-speed physical layer design in actual WPAN network scenario. The model facilitates the analysis of directional interference and coexistence unique to the millimeter-wave frequency band. Employing the developed model, we found that in order to generate minimum interference to the victim receiver, the interferer has to be angularly located at least 1.3 times the victim's beamwidth away from the victim's antenna pointing direction, and/or the interferer's antenna has to be angularly pointing towards at least 1.3 times its beamwidth away from the location of the victim. Additionally, to mitigate interference and still maintain the desired link connectivity, the victim receiver may shift its antenna beam away from the location of the interferer, as much as the angle between the victim's antenna pointing direction and the interferer's location minus 1.3 times the victim's beamwidth. Lastly, we have also introduced the quantification of coexistence availability between interfering and desired links, taking into consideration requirements and parameters in the physical layer.