Family-based study design is commonly used in gene mapping studies of complex human diseases. Most family-based studies use the transmission of alleles to assess evidence of association. It is generally believed that the transmission disequilibrium test (TDT) is robust against spurious association due to population stratification or admixture. While this is true when population stratification is due to discrete population structure, one should use the TDT-type methods with caution when they are applied to admixed populations in which population structure exists in local genomic regions. In a recently admixed population such as African Americans and Hispanic Americans, the linkage disequilibrium coefficient between a marker and disease loci in the parental generation contains a spurious component from the admixture process. In this paper, we show that the general belief that family-based design would guard against spurious association caused by population stratification does not always hold in admixed populations. It is safe to use the TDT as a test of association when population stratification is due to global genome ancestry difference. However, when population stratification is due to local ancestry difference in certain genomic regions, the use of the TDT as a test of association can lead to spurious association. Second, we present a statistical framework for fine mapping of disease associated genetic variants in admixed families. Unlike the TDT and other family-based association tests, this method does not rely on transmission disequilibrium, therefore can control local ancestry difference between transmitted and untransmitted alleles. Through simulations, we show that this method can control type I error rates under a wide range of population stratification mechanisms.