Emerging single cell technologies that simultaneously capture long-range interactions of genomic loci together with their DNA methylation levels are advancing our understanding of three-dimensional genome structure and its interplay with the epigenome at the single cell level. While methods to analyze data from single cell high throughput chromatin conformation capture (scHi-C) experiments are maturing, methods that can jointly analyze multiple single cell modalities with scHi-C data are lacking. Here, we introduce Muscle, a semi-nonnegative joint decomposition of Multiple single cell tensors, to jointly analyze 3D conformation and DNA methylation data at the single cell level. Muscle takes advantage of the inherent tensor structure of the scHi-C data, and integrates this modality with DNA methylation. We developed an alternating least squares algorithm for estimating Muscle parameters and established its optimality properties. Parameters estimated by Muscle directly align with the key components of the downstream analysis of scHi-C data in a cell type specific manner. Evaluations with data-driven experiments and simulations demonstrate the advantages of the joint modeling framework of Muscle over single modality modeling or a baseline multi modality modeling for cell type delineation and elucidating associations between modalities. Muscle is publicly available at https://github.com/keleslab/muscle.