DNA methylation is a fundamental element of epigenetic regulation that is governed by the MBD protein superfamily, a group of "readers" that share a highly conserved methyl-CpG-binding domain (MBD) and mediate chromatin remodeler recruitment, transcription regulation, and coordination of DNA and histone modification. Previous work has characterized the binding affinity and sequence selectivity of MBD-containing proteins toward palindromes of 5-methylcytosine (5mC) containing 5mCpG dinucleotides, often referred to as single symmetrically methylated CpG sites. However, little is known about how MBD binding is influenced by the prototypical local clustering of methylated CpG sites and the presence of DNA structural motifs encountered, e.g., during DNA replication and transcription. Here, we use Single-Molecule Kinetics through Equilibrium Poisson Sampling (SiMKEPS) to measure precise binding and dissociation rate constants of the MBD of human protein MBD1 to DNAs with varying patterns of multiple methylated CpG sites and diverse structural motifs. MBD binding is promoted by two major properties of its DNA substrates: 1) tandem (consecutive) symmetrically methylated CpG sites in double-stranded DNA and secondary structures in single-stranded DNA; and 2) DNA forks. Based on our findings, we propose a mechanistic model for how MBD proteins contribute to epigenetic boundary maintenance between transcriptionally silenced and active genome regions.