Carbonate rock dissolution during the reactive transport of carbon dioxide (CO2)-enriched brine has been studied extensively in the context of carbon storage in saline aquifers. However, there is limited knowledge of CO2-induced reactive transport in multiphase systems (containing oil and brine), which is more relevant to carbon sequestration in depleted oil reservoirs. In this work, we uncover the pore-scale dynamics of fluid flow and rock dissolution during carbonated water injection (CWI) in hydrophilic porous media containing two fluid phases (oil and brine). We combine novel core flooding and high-resolution imaging techniques to visualize and characterize changes in fluid occupancy and pore morphology. It is observed that the sequence of flow and transport in two-phase systems involves a pre-dissolution period, where CWI induces the displacement of waterflood-trapped oil, and a dissolution period typified by channel flow. Improved oil recovery during pre-dissolution emanates from an oil swelling mechanism that drives reconnection and mobilization of trapped oil globules. Additionally, CO2 is stored in both oil and carbonated water. Channel flow during dissolution results in the formation of wormholes with two distinct dissolution patterns. The first is a conical wormhole at lower injection rates where diffusion rates are significant. The second is a dominant wormhole at higher injection rates where advection dominates the transport of reactive species to the flow boundaries. We find that the oil displacement efficiency during dissolution is significantly lower than pre-dissolution levels and is dependent on the wormhole pattern, with dominant wormholes providing a high-permeability and high-velocity flow path for trapped oil movement. Therefore, unlike the injectivity losses that originate from salt precipitation during direct CO2 injection, CWI in depleted carbonate oil reservoirs enhances the injectivity of injection wells allowing for an energy efficient CO2 storage.