A drilling liner having a core bit at its bottom end is carried along with a pilot bit on an inner bottom hole assembly driven by a downhole mud motor. In one embodiment, the motor is powered by mud carried by an inner string. Alternatively, the inner string may be omitted and the flow of mud through the liner powers the motor: this requires a locking tool for locking the motor assembly to the outer assembly. Once an abnormally (high or low) pressured zone has been traversed, the liner is set as a casing, the inner assembly is pulled out, and drilling may be resumed using a conventional tool. Directional drilling is accomplished by having an MWD device for providing directional information and having directional devices on the inner and outer assembly. These include retractable steering pads. Expandable bits, under-reamers and jetting nozzles may also be used in the drilling process. One embodiment of the invention has a bottom thruster between the mud motor and the drill bits that makes it possible to continue drilling for a limited distance even if the upper portion of the casing is stuck.