When direct survey are about sensitive characteristics such as addiction to drugs, alcoholism, proneness to tax invasion and sexual violence, nonresponse bias and response bias become serious problems because people oftentimes do not wish to give true information. In this study, when the population is composed of strata such as gender, region, age group, we consider the simple model and crossed model by applying stratified random sampling which can estimate not only the domain population proportion but also the whole population proportion for two sensitive attributes such as drug use and sexual violence in the same time. In addition, when the size of each population stratum is unknown in stratified random sampling, we propose the simple model and crossed model by using stratified double sampling method. In each proposed survey design, the sample allocation of each stratum is dealt with in consideration of proportional allocation and optimal one. We compare the efficiency between the simple model and the crossed model according to the proposed stratified random sampling design.