Decays of the form B-s(0) -> J/psi K(s)(0)h(+)h((1)-) (h((1)) = K, pi) are searched for in proton-proton collision data corresponding to an integrated luminosity of 1.0 fb(-1) recorded with the LHCb detector. The first observation of the B-s(0) -> J/psi (KsK +/-)-K-0 pi(-/+) decay is reported, with significance in excess of 10 standard deviations. The B-0 -> J/psi (KsK+K-)-K-0 decay is also observed for the first time. The branching fraction of B-s(0) -> J/psi K(s)(0)h(+)h((1)-) is determined, to significantly better precision than previous measurements, using B-0 -> J/psi K(s)(0)h(+)h((1)-) as a normalisation channel. Branching fractions and upper limits of the other B-(s)(0) -> J/psi K-s(0)pi(+)pi(-) (s modes are determined relative to that of the B-0 -> J/psi K-s(0)pi(+)pi(-) decay.