Originally, progress towards the AI goal of building artificial agents with human-like intelligence was best seen in cognitive architecture research that focused on developing complete agents in a systematic, theory-driven way. Later, research in embodied AI and robotics turned away from this focus on higher-level cognition in favor of making robots robustly achieve simple tasks in the real world. The ensuing hiatus between cognition-focused and action-focused research perspectives is still reflected in cognitive and robotic architectures today. In this paper, we attempt to reunite the two views by introducing a theoretically motivated, generic interface between cognitive and robotic architectures. From this integration the advances in both cognitive and robotic architectures can be leveraged to produce more complex adaptive robotic behavior. We start by reviewing the differences between cognitive and robotic architecture, followed by a comparison of two alternative methods for integrating such architectures. As a result of this comparison, we propose a three-part interface framework for architecture integration. We then report two specific instances of the interface for integrating the ICARUS and ACT-R cognitive architectures into the robotic DIARC architecture, along with proof-of-concept implementations with two sets of knowledge structures for executing a simple office environment exploration task using a Pioneer P3-AT robot. We describe qualitative evaluations of both integrated architectures and discuss directions for future research with the proposed framework.