With the expanding size of three-dimensional (3D) seismic data, manual seismic interpretation becomes time consuming and labor intensive. For automating this process, the recent progress in machine learning, particularly the convolutional neural networks (CNNs), has been introduced into the seismic community and successfully implemented for interpreting seismic structural and stratigraphic features. In principle, such automation aims at mimicking the intelligence of experienced seismic interpreters to annotate subsurface geology both accurately and efficiently. However, most of the implementations and applications are relatively simple in their CNN architectures, which primary rely on the seismic amplitude but undesirably fail to fully use the pre-known geologic knowledge and/or solid interpretational rules of an experienced interpreter who works on the same task. A general applicable framework is proposed for integrating a seismic interpretation CNN with such commonly-used knowledge and rules as constraints. Three example use cases, including relative geologic time-guided facies analysis, layer-customized fault detection, and fault-oriented stratigraphy mapping, are provided for both illustrating how one or more constraints can be technically imposed and demonstrating what added values such a constrained CNN can bring. It is concluded that the imposition of interpretational constraints is capable of improving CNN-assisted seismic interpretation and better assisting the tasks of subsurface mapping and modeling.