Both excel and JMP generally handle time as numeric/continuous, but they differ in how they define the passage of time and the formatting options given to the user.(1=a day in excel and one second in JMP)
I didn't see a day of the month specified in your example, I'll assume that the 15th of the month will work and that you want to map the text to a numeric date. The text can be copied into a formula and the comments (preceded by //) will disappear.
Informat( //transform text to a numeric format
"15" || //add the 15th of the month
Munger( :Text_Mon_Yr, 1, 3 ) || // Extract the first three characters as the month abbrev
"20" || //add 20 to the year (assumes all years after 1999)
Munger( :Text_Mon_Yr, 5, 2 ), //adds the second half of the year code
"ddMonyyyy" // the jmp format to transform[informat] from text to numeric
)