When people think of everyday things like an egg, they typically have a mental image associated with it. This allows them to correctly judge, for example, that "the yolk surrounds the shell" is a false statement. Do language models similarly have a coherent picture of such everyday things? To investigate this, we propose a benchmark dataset consisting of 100 everyday things, their parts, and the relationships between these parts, expressed as 11,720 "X relation Y?" true/false questions. Using these questions as probes, we observe that state-of-the-art pre-trained language models (LMs) like GPT-3 and Macaw have fragments of knowledge about these everyday things, but do not have fully coherent "parts mental models" (54-59\% accurate, 19-43\% conditional constraint violation). We propose an extension where we add a constraint satisfaction layer on top of the LM's raw predictions to apply commonsense constraints. As well as removing inconsistencies, we find that this also significantly improves accuracy (by 16-20\%), suggesting how the incoherence of the LM's pictures of everyday things can be significantly reduced.