In multiorbital materials, superconductivity can exhibit new exotic forms that include several coupled condensates. In this context, quantum confinement in two-dimensional superconducting oxide interfaces offers new degrees of freedom to engineer the band structure and selectively control 3d-orbitals occupancy by electrostatic doping. However, the presence of multiple superconducting condensates in these systems has not yet been demonstrated. Here, we use resonant microwave transport to extract the superfluid stiffness of the (110)-oriented LaAlO3/SrTiO3 interface in the entire phase diagram. We evidence a transition from single-band to two-band superconductivity driven by electrostatic doping, which we relate to the filling of the different 3d-orbitals based on numerical simulations of the quantum well. Interestingly, the superconducting transition temperature decreases while the second band is populated, which challenges the Bardeen-Cooper-Schrieffer theory. To explain this behaviour, we propose that the superconducting order parameters associated with the two bands have opposite signs with respect to each other.