Processes that involve the transport of charged species and the simultaneous fluid flow of multiple constituents and phases, like liquids and gases, are very important in the areas of energy, manufacturing, and healthcare. They occur commonly in energy conversion, energy storage, catalysis, manufacturing, and bioengineering processes. Practical examples of such processes include electrolysis for hydrogen production, electrodialysis for water desalination, gas diffusion electrodes for chemical conversion, and carbon capture, as well as several other processes that have a direct impact on sustainability and climate resilience. A comprehensive modeling framework can significantly accelerate the exploration and understanding of these complex multiphase electrochemical processes for applications like efficient water electrolysis for green hydrogen production and cheaper, lightweight dialysis machines. We present a modeling framework for coupling the electrokinetics of charged species with multiphase flows. We use a phase-field approach to model the fluid-fluid interfaces based on the Cahn-Hilliard equations coupled with mixture momentum equations called the Cahn-Hilliard-Navier-Stokes (CHNS) system. The charge transport of ions is modeled using Poisson-Nernst-Planck (PNP) equations. We present a detailed coupling strategy between CHNS and PNP equations derived based on mixture theory, rational continuum mechanics, and energy dissipation laws. Although the focus will be primarily on the modeling framework, we will present some preliminary numerical tests of the models proposed.