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+ → KS0π+, Λc+ → pKS0 and Λc+ → Λπ+, 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 < pT (D+,Λc+ ) < 10GeV, |η(D+,Λc+ )| < 1.6, 1.5 < Q2 < 1000GeV2 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 Λc+ baryons is extracted.