The increasing prevalence of finite element (FE) simulations in the study of atherosclerosis has spawned numerous inverse FE methods for the mechanical characterization of diseased tissue in vivo. Current approaches are however limited to either homogenized or simplified material representations. This paper presents a novel method to account for tissue heterogeneity and material nonlinearity in the recovery of constitutive behavior using imaging data acquired at differing intravascular pressures by incorporating interfaces between various intra-plaque tissue types into the objective function definition. Method verification was performed in silico by recovering assigned material parameters from a pair of vessel geometries: one derived from coronary optical coherence tomography (OCT); one generated from in silico-based simulation. In repeated tests, the method consistently recovered 4 linear elastic (0.1 +/- 0.1% error) and 8 nonlinear hyperelastic (3.3 +/- 3.0% error) material parameters. Method robustness was also highlighted in noise sensitivity analysis, where linear elastic parameters were recovered with average errors of 1.3 +/- 1.6% and 8.3 +/- 10.5%, at 5% and 20% noise, respectively. Reproducibility was substantiated through the recovery of 9 material parameters in two more models, with mean errors of 3.0 +/- 4.7%. The results highlight the potential of this new approach, enabling high-fidelity material parameter recovery for use in complex cardiovascular computational studies.