The irreversibility line H_irr, cannot cross H_c1, and the temperature dependence of H_irr(T) differs from H_c1(T). Therefore there exists an intersection between them, and it is expected that the simple power-law behaviour of the irreversibility line H_irr(T)~(1-T/T_c)^alpha will break down over a wide range of temperature. We have observed this interesting phenomenon in our three YBa₂Cu₃O₇/PrBa₂Cu₃O₇ (YBCO/PrBCO) multilayer thin films with different YBCO superconducting layers for the first time due to the enhancement of H_c1 in a parallel (|| CuO plane) magnetic field. The temperature dependence of H_c1(T) in these three films is in good agreement with calculations of the enhanced H_c1 derived from the London approximation for the case of a slab of thickness tau which is thinner than the London penetration depth lambda , when the applied field is parallel to the sample surface, and they mimic the results observed by Civale and co-workers in thinner pure YBCO ultra-thin films (~25 nm).