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We report high-resolution neutron diffraction on the new heavy fermion material Ce₃TiSb₅. Ce₃TiSb₅ exhibits an antiferromagnetic order below T_N = 5.5 K. Our specific heat and magnetic susceptibility measurements as a function of magnetic field reveal a phase diagram with three distinct magnetic phases. Using neutron diffraction we study the magnetic structure throughout the phase diagram, and uncover a multi-k spin structure in the intermediate field phase. Magnetic multi-k structures are of current interest because they are an important ingredient for topologically non-trivial properties. Finally, our measurements demonstrate that the high-field magnetic phase exhibits inverse melting, where the magnetically ordered state becomes disordered upon cooling. This is highly unconventional behavior and suggests that the complex magnetic order of Ce₃TiSb₅ is driven via the competition of several degrees of freedom.