No simple model exists that accurately describes the melting behavior and breathing dynamics of double-stranded DNA as a function of nucleotide sequence. This is especially true for homogenous and periodic DNA sequences, which exhibit large deviations in melting temperature from predictions made by additive thermodynamic contributions. Currently, no method exists for analysis of the DNA breathing dynamics of repeats and of highly G/C- or A/T-rich regions, even though such sequences are widespread in vertebrate genomes. Here, we extend the nonlinear Peyrard-Bishop-Dauxois (PBD) model of DNA to include a sequence-dependent stacking term, resulting in a model that can accurately describe the melting behavior of homogenous and periodic sequences. We collect melting data for several DNA oligos, and apply Monte Carlo simulations to establish force constants for the 10 dinucleotide steps (CG, CA, GC, AT, AG, AA, AC, TA, GG, TC). The experiments and numerical simulations confirm that the GG/CC dinucleotide stacking is remarkably unstable, compared with the stacking in GC/CG and CG/GC dinucleotide steps. The extended PBD model will facilitate thermodynamic and dynamic simulations of important genomic regions such as CpG islands and disease-related repeats.