The aim of the paper is to introduce and study a new class of spaces called mildly (1, 2)∗ -normal spaces and a new class of functions called (1, 2)∗ -rg-continuous, (1, 2)∗ - R-map, almost (1, 2)∗ -continuous function and almost (1, 2)∗ -rg-closed function in bitopological spaces. Subsequently, the relationships between mildly (1, 2)∗ -normal spaces and the new bitopological functions are investigated. Moreover, we obtain characterizations of mildly (1, 2)∗ -normal spaces, properties of the new bitopological functions and preservation theorems for mildly (1, 2)∗ -normal spaces in bitopological spacesThe aim of the paper is to introduce and study a new class of spaces called mildly (1, 2)∗ -normal spaces and a new class of functions called (1, 2)∗ -rg-continuous, (1, 2)∗ - R-map, almost (1, 2)∗ -continuous function and almost (1, 2)∗ -rg-closed function in bitopological spaces. Subsequently, the relationships between mildly (1, 2)∗ -normal spaces and the new bitopological functions are investigated. Moreover, we obtain characterizations of mildly (1, 2)∗ -normal spaces, properties of the new bitopological functions and preservation theorems for mildly (1, 2)∗ -normal spaces in bitopological spaces.