In applications of predictive modeling, such as insurance pricing, indirect or proxy discrimination is an issue of major concern. Namely, there exists the possibility that protected policyholder characteristics are implicitly inferred from non-protected ones by predictive models, and are thus having an undesirable (or illegal) impact on prices. A technical solution to this problem relies on building a best-estimate model using all policyholder characteristics (including protected ones) and then averaging out the protected characteristics for calculating individual prices. However, such approaches require full knowledge of policyholders' protected characteristics, which may in itself be problematic. Here, we address this issue by using a multitask neural network architecture for claim predictions, which can be trained using only partial information on protected characteristics, and it produces prices that are free from proxy discrimination. To test this model, we use two datasets: a synthetic health insurance portfolio, as well as an extensive non-life motor pricing dataset, containing two protected covariates. We demonstrate the use of the proposed model and we find that its predictive accuracy is similar to a conventional feedforward neural network (on full information). However, this multi-task network has clearly superior performance in the case of partially missing policyholder information.