The branching fraction of D+ -> K-S(0)pi(0)e(+)nu(e) is measured for the first time using 7.93 fb(-1) of e(+)e(-) annihilation data collected at the center-of-mass energy root s = 3.773 GeV with the BESIII detector operating at the BEPCII collider, and is determined to be B(D+ -> K-S(0)pi(0)e(+)nu(e)) = (0.881 +/- 0.017(stat.) +/- 0.016(syst.))%. Based on an analysis of the D+ -> K-S(0)pi(0)e(+)nu(e) decay dynamics, we observe the S-wave and P-wave components with fractions of f(S-wave) = (6.13 +/- 0.27(stat.) +/- 0.30(syst.))% and f((K) over bar*(892)0) = (93.88 +/- 0.27(stat.) +/- 0.29(syst.))%, respectively. From these results, we obtain the branching fractions B(D+ -> (K-S(0)pi(0))(S-wave) e(+)nu(e)) = (5.41 +/- 0.35(stat.) +/- 0.37(syst.)) x 10(-4) and B(D+ -> (K) over bar*(892)(0)e(+)nu(e)) = (4.97 +/- 0.11(stat.) +/- 0.12(syst.))%. In addition, the hadronic form-factor ratios of D+ -> (K) over bar*(892)(0)e(+)nu(e) at q(2) = 0, assuming a single-pole dominance parameterization, are determined to be r(V) = V(0)/A(1)(0) = 1.43 +/- 0.07(stat.) +/- 0.03(syst.) and r(2) = A(2)(0)/A(1)(0) = 0.72 +/- 0.06(stat.) +/- 0.02(syst.).