The transmission properties of one-dimensional photonic crystals containing double-negative and single-negative materials are studied theoretically. A special kind of photonic band gap is found in this structure. This gap is invariant with scaling and insensitive to thickness fluctuation. But when changing the ratio of the thickness of two media, the width of the gap could be enlarged. The defect modes are analyzed by inducing a linear defect layer in the structure. It is found that the number of defect modes will increase when the thickness of the defect layer becomes larger.