A conservative lattice Boltzmann solver with phase-field approach is presented to capture the interface for multiphase flows. The phase field solver is based on the conservative Allen-Cahn equation. The lattice Boltzmann implementation uses a multiple-relaxation time (MRT) technique on a D3Q27 lattice. The scattering operator is formulated in a central momentum space using the macroscopic velocity. Such a transformation allows for Galilean invariance and a stable numerical scheme. A set of benchmark problems for two-fluid flows is examined to demonstrate the robustness and accuracy by comparing against other published front tracking algorithms. Specifically, the vortex in a box and rising bubble under normal gravity conditions are simulated and compared against other high resolution methods published in the literature. Further, the lattice structure for the solver is created on an octree platform, thereby providing an excellent platform to solve multi-scale problems with dynamic adaptive refinement. The octree structure can be refined both spatially and temporally allowing maintenance of a constant CFL condition, improving numerical accuracy and stability.