Can you use a percentage as an independent variable in multiple linear regression? I'm having difficulty finding a definitive way to determine whether I can use a percentage measure as an independent variable in multiple linear regression or not.
From my understanding, the percentage can't be considered a true continuous measure for some reason and violates some assumptions of the regression model.
Edit 1: For example, I have seen the argument that percentage data is discrete because the underlying data that the percentages are calculated from is discrete. 
Can someone explain why percentages aren't true continuous measures and in what cases I could use a percentage as an independent variable?
Edit 2: For further clarity, I will explain what I'm hoping to accomplish specifically below here. The goal is to use a dependent variable (length of time) and claim it explained by several independent variables (some dummies, one a percentage that isn't restricted to any certain values for any observation). I know the assumption for linear regression is that the independent variables will be continuous measures, which is why I utilize dummy variables for the dichotomous categorical variables. I'm just trying to make sure I don't need to utilize a different analytical technique altogether because of the percentages being technically discrete (is this even necessarily true?).
Edit 3: In the interest of complete specificity,
DV - Length of maternity leave taken.
IV's - percentage of normal salary paid by employer during leave, and other dummies not relevant to the question.
 A: Percentages can be considered continuous on the interval [0,1].  There is no reason why percentages can't be independent variables in linear regression.  In fact, there is no requirement that independent variables need to be continuous.  Indicator variables are often used as independent variables in regressions.
A: The assumption of normality to which you refer does not apply to any of the predictors (after all how could a binary predictor be normal?) nor does it apply to the outcome. What it applies to is the residuals from your model. So at this stage before you have fitted the model you do not know whether it holds or not. Similarly the usual check for homoscedasticity is based on looking at the residuals in a plot against the fitted values. The question of continuity is more subtle but no measured variable even if theoretically continuous is going to be so when actually measured to finite precision.
If I was modelling length of stay I would be more worried about the skew and also the issue of whether some have been censored because they have not returned to work yet. Have you considered using a time to event model (also known as the Cox model or proportional hazards)?
Another concern, depending on the rules in your jurisdiction, is that if maternity pay is at a certain level for $j$ moths, a lower level for $k$ months, and the stops, you will get bunching of values at $j$ and $k$ (I would have thought).
A: Suppose you have a model
$$Y = B_1 X_1 + B_2 X_2 + E,$$
where $E \sim Nor(0,1)$
Let $X_3$, $X_4$ be the percentages and $S_1$, $S_2$ be the total of $X_1$, $X_2$ respectively
then, $X_3 = X_1/S_1*100$ and $X_4 = X_2/S_2*100$.
Then the model with percentage will be,
$Y = B_3 X_3 + B_4 X_4 + E'$
The estimates will be $B = ((X'X)^{-1})X'Y$ and the relation between the estimates are,
$B_3 = B_1/S_1*100$ and $B_4 = B_2/S_2*100$.
