Drug combinations have been shown to be an effective strategy for cancer therapy, but identifying beneficial combinations through experiments is labor-intensive and expensive Machine learning (ML) systems that can propose novel and effective drug combinations have the potential to dramatically improve the efficiency of combinatoric drug design.{However, the biophysical parameters of drug combinations are degenerate, making it challenging to identify the ground truth of drug interactions even given high-quality experimental data. Existing ML models are highly underspecified to meet this challenge, leaving them vulnerable to producing parameters that are not biophysically realistic and harming generalization.We have developed a new ML model, ``ComboPath,'' to predict the cellular dose-response surface of a two-drug combination based on each drug's interactions with their known protein targets. {ComboPath incorporates a biophysically-motivated intermediate parameterization with prior information used to improve model specification. This} is the first ML model to nominate beneficial drug combinations while simultaneously reconstructing the dose-response surface, providing insight into both the potential of a drug combination and its optimal dosing for therapeutic development. We show that our models were able to accurately reconstruct 2D dose response surfaces across held-out combination samples from the largest available combinatoric screening dataset while {substantially improving model specification for key biophysical parameters}