The band structures of one-dimensional photonic crystals containing a defect layer with a negative refractive index are studied, showing that the defect modes possess three types of dispersion: positive, zero, and negative types. Based on these three types of dispersion, practical designs for large incident angle filters without polarization effect and for narrow frequency and sharp angular filters are suggested. Moreover, the splitting of one degenerate defect mode into multiple defect modes is observed in the band gap when the parameters of the defect layer vary. This mode splitting phenomenon can be used to design multiple channeled filters or filters with a rectangular profile. The dispersion multiplicity of the defect modes can be understood by an approximate formula, and the critical condition for the defect mode splitting is also analyzed. Based on these analyses, practical optimization design of omnidirectional filter is also suggested.