We report a study of D(*)(sJ)(2317)(+) and D(sJ)(2460)(+) meson production in B decays. We observe the decays B+-->D((*)+)(sJ)D ((*)0) and B0-->D((*)+)(sJ)D((*)-) with the subsequent decays D(*)(sJ)(2317)(+)-->D(+)(s)pi(0), D(sJ)(2460)(+)-->D(+)(s)gamma, and D(sJ)(2460)(+)-->D(*+)(s)pi(0). Based on a data sample of 122.1 x 10(6) BB pairs collected with the BABAR detector at the PEP-II B factory, we obtain branching fractions for these modes, including the previously unseen decays B-->D((*)+)(sJ)D(*). In addition, we perform an angular analysis of D(sJ)(2460)(+)-->D(+)(s)gamma decays to test the different D(sJ)(2460)(+) spin hypotheses.