There is such a thing as a multiple correlation coefficient, although almost no one seems to know it exists. In addition, it does not come standard with output from any statistical software, as far as I know. So I suspect that you are looking at $R^2$, as @StephanKolassa suggests. You can think of this as the proportion of the variance in your DV that your model helps to explain. Unless something has gone horribly awry (see, e.g., When is $R^2$ negative?), this value will always be positive (you can't explain less than zero of what's going on).
For what it's worth, the multiple correlation coefficient is the correlation between your model's predicted values, $\hat y$, and the actual values of your DV, $y$. Again, unless your model is badly misspecified, the procedure used to fit your model coefficients works in such a way that this will always be positive, even if the individual coefficients / correlations are negative. In other words, when a data point has a higher (lower) value, your model predicts a higher (lower) value, even if this occurs when $x$ is at a lower (higher) value.
Here is a simple demonstration using only one variable to make it easier to see. I don't know if you are familiar with the statistical software
R, but hopefully the code is sufficiently self-explanatory.
set.seed(3293) # this makes the example exactly reproducible
x = rnorm(20, mean=5, sd=1) # these generate random data for x & y
y = 9 - 1*x + rnorm(20, mean=0, sd=1)
model = lm(y~x) # here I fit a simple linear regression
cor(x, y) # this is the correlation between x & y
#  -0.6276509
cor(fitted(model), y) # this is the correlation w/ the model's predicted values
#  0.6276509
summary(model) # here is the model output, the coefficient is -, but R2 is +
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 9.0107 1.4055 6.411 4.91e-06 ***
# x -1.0144 0.2966 -3.421 0.00305 **
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# Residual standard error: 1.298 on 18 degrees of freedom
# Multiple R-squared: 0.3939, Adjusted R-squared: 0.3603
# F-statistic: 11.7 on 1 and 18 DF, p-value: 0.003049
Below is what this looks like. Notice that you have lower
y values associated with higher
x values, but that higher
y values are associated with higher
fitted y values.