The present work devises and implements numerical procedures to simulate multiphase flows where precise prediction of these interfaces is essential. A three-phase flow model with two fluids and a solid phase involving two moving interfaces, i.e. fluid-fluid (F-F) and fluid-solid (F-S) interfaces, is proposed. Two limiting cases of the model are two-fluid flow and fluid-solid flow. The F-F interface is captured using a level-set method. Two mass conservation schemes, i.e. Global (GMC) and Local (LMC) Mass Correction Schemes, are presented to ensure mass conservation. While GMC is for general two-fluid flow problems, LMC is developed for stratified two-fluid flows. Artificial viscosity is introduced in selected region away from the F-F interface during the advection of the level-set function and shown to improve numerical stability. A new fixed-grid F-S interface tracking technique is proposed. Solids, represented by local distance functions, are tracked explicitly. The procedure can handle flows with multiple complex shaped solids. The F-F interface tracking procedure is extended to the case where there is a slip velocity at the solid surfaces as encountered in the modeling of electrophoresis of particles. A set of combined conservation equations is employed for the physical domain consists of the three phases. Surface tension effects at the F-F interface, both curvature and Marangoni driven, are incorporated using the Continuum Surface Force model. Solution of the governing equations together with the F-F interface capturing and F-S interface tracking procedures are implemented in a finite volume method. Validation of the present model is made against available results in two-fluid and fluid-solid flows. The applications of the present model in a large variety of multiphase flow problems are demonstrated.