Multipolar, multi-lumen, virtual-electrode catheters having at least one surface electrode, and methods for treatment (e.g., treatment of cardiac arrhythmias) with such catheters are disclosed. The catheters have at least two internal lumens, and at least one internal, flexible electrode rides in each internal lumen. The flexible electrodes carry treatment energy (e.g., radiofrequency energy). The energy exits the catheters via at least one exit feature (e.g., slots, portholes, or micro-pores). The methods for treatment include operating the catheters in different modes depending upon location and type of treatment to be performed. The treatment energy delivered by one of the internal, flexible electrodes may be directed to the other internal, flexible electrode; or the energy delivered by one or both of the internal, flexible electrodes may be directed to one or more surface electrodes. The delivered energy establishes at least one electric field, and possibly one or more lesions, in the tissue.