The dynamics of tumor-immune interactions within a complex tumor microenvironment are typically modeled using a system of ordinary differential equations or partial differential equations. These models introduce some unknown parameters that need to be estimated accurately and efficiently from the limited and noisy experimental data. Moreover, due to the intricate biological complexity and limitations in experimental measurements, tumor-immune dynamics are not fully understood, and therefore, only partial knowledge of the underlying physics may be available, resulting in unknown or missing terms within the system of equations. In this study, we develop a cancer biology-informed neural network model(CBINN) to infer the unknown parameters in the system of equations as well as to discover the missing physics from sparse and noisy measurements. We test the performance of the CBINN model on three distinct nonlinear compartmental tumor-immune models and evaluate its robustness across multiple synthetic noise levels. By harnessing these highly nonlinear dynamics, our CBINN framework effectively estimates the unknown model parameters and uncovers the underlying physical laws or mathematical structures that govern these biological systems, even from scattered and noisy measurements. The models chosen here represent the dynamic patterns commonly observed in compartmental models of tumor-immune interactions, thereby validating the generalizability and efficacy of our methodology.