In this paper, we have proposed a family of combined-type estimators of the population mean in stratified random sampling using the information on an auxiliary variable under the situation in which non-response is observed on both study and auxiliary variables. In order to propose the family, we have adopted the idea of two-phase sampling scheme when the population mean of auxiliary variable is not known. The expressions for the bias and mean square error of the proposed family up to the first degree of approximation have been derived. A theoretical study on the cost of the survey has also been carried out. A numerical illustration has been presented to hold up the theoretical results.