Bernoulli Naive bayes does not assume gaussian distribution of all continuous features, because it does not make sense. Gaussian Naive Bayes assumes gaussian distribution for continuous features and it is the appropriate way for using Naive Bayes approach if you have continuous features.
On the other hand, if you have binary categorical data then the appropriate approach is Bernoulli Naive Bayes. If your features are categorical but not binary then you could transform them into binary categorical using dummy boolean variables for each available value of the categorical features. The main point of Naive Bayes algorithm is the assumption of feature independence, which in some real world classification problems does not hold.
You need to specify a conditional probability p(x|y) of the feature value x given the class label y. Since Naive Bayes assumes that all features are conditionally independent given the class, you can mix different likelihood models for each feature considering any prior knowledge about it.
For example, considering a continuous feature you might assume that p(x|y) is normally distributed, then you can stimate the mean and variance for this feature under each class in the training set and after that you can use the PDF of the Normal Distribution to estimate p(x|y).
Considering another feature which is categorical, you can estimate p(x|y) using a Bernoulli or multinomial event model and multiply the two conditional probabilities together in the final prediction (since they are assumed to be independent anyway).