We report measurements of the properties of the D(+)(sJ)(2317) and D(+)(sJ)(2457) resonances produced in continuum e(+)e(-) annihilation near sqrt[s]=10.6 GeV. The analysis is based on an 86.9 fb(-1) data sample collected with the Belle detector at KEKB. We determine the masses to be M(D(+)(sJ)(2317))=2317.2+/-0.5(stat)+/-0.9(syst) MeV/c(2) and M(D(+)(sJ)(2457))=2456.5+/-1.3(stat)+/-1.3(syst) MeV/c(2). We observe the radiative decay mode D(+)(sJ)(2457)-->D(+)(s)gamma and the dipion decay mode D(+)(sJ)(2457)-->D(+)(s)pi(+)pi(-) and determine their branching fractions. No corresponding decays are observed for the D(sJ)(2317) state. These results are consistent with the spin-parity assignments of 0(+) for the D(sJ)(2317) and 1(+) for the D(sJ)(2457).