The collision of a bubble at liquid liquid, solid-liquid-liquid, and gas-liquid-liquid interfaces, the latter two of which are referred to as compound interfaces, is modeled to predict the bubble's velocity profile and the pressure buildup and drainage rate of the film(s) formed at impact. A force balance approach, previously outlined for bubble collisions at solid and free surfaces, is employed, which takes into account four forces acting on the bubble: buoyancy, drag, inertia of the surrounding liquid through an added mass force, and a film force resulting from the pressure buildup in the liquid film formed between the bubble and the interface upon impact. The augmented Young-Laplace equation is applied to define the pressure buildup in the film(s), while lubrication theory is employed to define the film drainage rate(s) through the use of the Stokes-Reynolds equation. This is the first time this modeling technique has been implemented for bubble collisions with these interface types as all previous models have relied only on grid-based simulations. The models were validated through experiments conducted here with water and silicone oils of various viscosities and from data found in literature. A reasonable agreement is observed between the theoretical and experimental velocity profiles found for these liquid combinations under varying conditions of impact velocity and top film thickness. The spatiotemporal film thickness and pressure profile evolution, features not yet able to be captured through experiment, are also presented and discussed.