How about
$$ \Delta M = 12 (Y - Y_0) + (M - M_0) + [D \ge D_0], $$
where $Y$, $M$ and $D$ are the current year, month and day numbers, $Y_0$, $M_0$ and $D_0$ are the year, month and day of the starting date, $\Delta M$ is the calculated number of months elapsed since the starting date (rounded up) and $[Q]$ is the Iverson bracket, i.e. $1$ if the condition $Q$ is true and $0$ otherwise.
In effect, $\Delta M$ is incremented by one at the start of the $D_0$-th day of each month, unless the month has less than $D_0$ days, in which case the increment happens at the start of the first day of the next month.