A new three-phase model of compressible two-fluid flows in a deformed porous medium is presented. The derivation of the model is based on the application of the Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems theory to three-phase solid-fluid mixture. The resulting governing equations are hyperbolic and satisfy the laws of irreversible thermodynamics - conservation of energy and growth of entropy. Due to these properties, the formulated model is well suited for the straightforward application of advanced high accuracy numerical methods applicable to the solution of hyperbolic systems, and ensures the reliability of the numerically obtained solutions. On the basis of the formulated nonlinear model, the governing equations for the propagation of small-amplitude waves are obtained, allowing the use of an efficient finite-difference scheme on staggered grids for their numerical solution. Some numerical examples are presented showing the features of wave propagation in a porous medium saturated with a mixture of liquid and gas with their different ratios.