We report the results of muon spin rotation and relaxation (μSR) measurements on the recently discovered layered Cu-based superconducting material La 2 (Cu 1−x Ni x ) 5 As 3 O 2 (x = 0.40 and 0.45). Transverse-field μSR experiments on both samples show that the temperature dependence of superfluid density is best described by a two-band model. The absolute values of zero-temperature magnetic penetration depth λ ab (0) were found to be 427(1.7) and 422(1.5) nm for x = 0.40 and 0.45, respectively. Both compounds are located between the unconventional and the standard BCS superconductors in the Uemura plot. No evidence of time-reversal symmetry breaking in the superconducting state is suggested by zero-field μSR measurements.