Encoding quantum information in quantum states with disjoint wave-function support and noise insensitive energies is the key behind the idea of qubit protection. While fully protected qubits are expected  to  offer  exponential  protection  against  both  energy  relaxation  and  pure  dephasing, simpler circuits may grant partial protection with currently achievable parameters. Here, we study a fluxonium circuit in which the wave-functions are engineered to minimize their overlap while benefiting  from  a  first-order-insensitive  flux  sweet  spot.  Taking  advantage  of  a  large superinductance  (L  ∼   1  μH),  our  circuit  incorporates  a  resonant  tunneling  mechanism  at  zero
external flux that couples states with the same fluxon parity, thus enabling bifluxon tunneling. The states |0 ⟩  and |1 ⟩  are encoded in wave-functions with parities 0 and 1, respectively, ensuring a minimal  form  of  protection  against  relaxation.  Two-tone  spectroscopy  reveals  the  energy  level structure of the circuit and the presence of 4π quantum-phase slips between different potential wells corresponding to m = ±1 fluxons, which can be precisely described by a simple fluxonium Hamiltonian or by an effective bifluxon Hamiltonian. Despite suboptimal fabrication, the measured relaxation  (T 1   =  177  ±  3  μs)  and  dephasing  (T E 2   =  75  ±  5  μs)  times  not  only  demonstrate  the relevance of our approach but also opens an alternative direction towards quantum computing using partially-protected fluxonium qubits.