Charm production in deep inelastic scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 120 pb(-1). The hadronic decay channels D+ -> K-S(0)pi(+), Lambda(+)(c) -> pK(S)(0) and Lambda(+)(c) -> Lambda pi(+), and their charge conjugates, were reconstructed. The presence of a neutral strange hadron in the final state reduces the combinatorial background and extends the measured sensitivity into the low transverse momentum region. The kinematic range is 0 < p(T) ( D+, Lambda(+)(c)) < 10GeV, vertical bar eta( D+,Lambda(+)(c))vertical bar < 1.6, 1.5 < Q(2) < 1000GeV(2) and 0.02 < y < 0.7. Inclusive and differential cross sections for the production of D+ mesons are compared to next-to-leading-order QCD predictions. The fraction of c quarks hadronising into Lambda(+)(c) baryons is extracted.