A reactor containing a heat exchanger is disclosed, which can be operated with co-current or counter-current flow. Also disclosed is a system that includes a reactor having a reformer and a vaporizer, a fuel supply, and a water supply. The reactor includes a source of combustion gas, a reformer operative to receive reformate, and a vaporizer operative to receive water. The reformer and vaporizer each include a stack assembly formed by a combination of separator shims and channel shims. The separator shims and channel shims are stacked in a regular pattern to form two sets of channels within the stack assembly. One set of channels will have vertical passageways at either end and a horizontal flowpath between them, while the other set of channels has only a horizontal flowpath.