Both maternal and paternal disease history can be important predictors of the risk of common conditions such as heart disease or cancer because of shared environmental and genetic risk factors. Sometimes maternal and paternal history can have remarkably different effects on offspring's status. The results are often affected by how the maternal and paternal disease histories are quantified. We proposed using the log-rank score (LRS) to investigate the separate effect of maternal and paternal history on diseases, which takes parental disease status and the age of their disease onset into account. Through simulation studies, we compared the performance of the maternal and paternal LRS with simple binary indicators under two different mechanisms of unbalanced parental effects. We applied the LRS to a national cohort study to further segregate family risks for heart diseases. We demonstrated using the LRS rather than binary indicators can improve the prediction of disease risks and better discriminate the paternal and maternal histories. In the real study, we found that the risk for stroke is closely related with maternal history but not with paternal history and that maternal and paternal disease history have similar impact on the onset of myocardial infarction.