Identifying genomic regions with functional genomic properties that are conserved between human and mouse is an important challenge in the context of mouse model studies. To address this, we develop a method to learn a score of evidence of conservation at the functional genomics level by integrating information from a compendium of epigenomic, transcription factor binding, and transcriptomic data from human and mouse. The method, Learning Evidence of Conservation from Integrated Functional genomic annotations (LECIF), trains neural networks to generate this score for the human and mouse genomes. The resulting LECIF score highlights human and mouse regions with shared functional genomic properties and captures correspondence of biologically similar human and mouse annotations. Analysis with independent datasets shows the score also highlights loci associated with similar phenotypes in both species. LECIF will be a resource for mouse model studies by identifying loci whose functional genomic properties are likely conserved.