Chromatin is the driver of gene regulation, yet understanding the molecular interactions underlying chromatin factor combinatorial patterns (or the "chromatin codes") remains a fundamental challenge in chromatin biology. Here we developed a global modeling framework that leverages chromatin profiling data to produce a systems-level view of the macromolecular complex of chromatin. Our model ultilizes maximum entropy modeling with regularization-based structure learning to statistically dissect dependencies between chromatin factors and produce an accurate probability distribution of chromatin code. Our unsupervised quantitative model, trained on genome-wide chromatin profiles of 73 histone marks and chromatin proteins from modENCODE, enabled making various data-driven inferences about chromatin profiles and interactions. We provided a highly accurate predictor of chromatin factor pairwise interactions validated by known experimental evidence, and for the first time enabled higher-order interaction prediction. Our predictions can thus help guide future experimental studies. The model can also serve as an inference engine for predicting unknown chromatin profiles--we demonstrated that with this approach we can leverage data from well-characterized cell types to help understand less-studied cell type or conditions.