sklearn: sklearn.linear_model.HuberRegressor vs sklearn.linear_model.ElasticNet
Yes, many loss functions in regression models are using a combination of L1 and L2 for different purposes. To realize the difference, I start with Ridge regression. 

Ridge regression addresses some of the problems of Ordinary Least Squares by imposing a penalty on the size of the coefficients. The ridge coefficients minimize a penalized residual sum of squares. 

The HuberRegressor is different to Ridge because it applies a linear loss to samples that are classified as outliers. A sample is classified as an inlier if the absolute error of that sample is lesser than a certain threshold.

ElasticNet is a linear regression model trained with both $\iota_1$ and $\iota_2$-norm regularization of the coefficients. This combination allows for learning a sparse model where few of the weights are non-zero like Lasso, while still maintaining the regularization properties of Ridge. Elastic-net is useful when there are multiple features which are correlated with one another. Lasso is likely to pick one of these at random, while elastic-net is likely to pick both.