Lineage-based haplotype markers (e.g., Y chromosome STRs and mitochondrial DNA sequences) are important adjunct tools to the autosomal markers for kinship analysis and for specialized kinship applications such as database searching. Traditionally, the prosecution or kinship hypothesis considers the haplotypes in the same lineage and the probability of genotype data given the lineage hypothesis is simply set at 1 if the number of mismatched loci or nucleotides between the questioned person and the references is less than a predefined threshold. In this study, a kinship hypothesis based on a fixed relationship of the questioned person in the reference family is introduced. A graphical model is proposed to calculate the probability of the genotype data given the kinship hypothesis, which is the product of haplotype frequency of the founder in the pedigree and the transmission probability from the founder to all descendants. Proper mutation models are suggested for Y chromosome STRs and mitochondrial DNA sequence variants (i.e., SNPs) to calculate the transmission probability. The methods to infer the genotypes of the untyped individuals in the pedigree and the computational complexity of handling these untyped individuals are also addressed. Lastly, numerical examples of the applications are given to demonstrate the kinship hypothesis and the algorithms.