From the gbm package documentation:
interaction.depth: "Integer specifying the maximum depth of each tree (i.e., the highest level of variable interactions allowed). A value of 1 implies an additive model, a value of 2 implies a model with up to 2-way interactions, etc. Default is 1."
And for more details there is this question on what exactly interaction.depth is, which basically says "Package GBM uses
interaction.depth parameter as a number of splits it has to perform on a tree (starting from a single node)".
But note that for every split you make the tree increases its depth. So while interaction.depth in GBM and max_depth in H2O may not be exactly the same thing the numbers map pretty well (i.e. interaction.depth=1 will grow a tree as deep as max_depth=1 in H2O-3), and
max_depth is the closest option you have to
Here are a few images to illustrate what max_depth looks like in H2O-3, but as the linked question suggests, you should use
pretty.gbm.tree function to explore exactly what interaction.depth does since the R GBM does not build trees the same way H2O-3 does (for example R GBM builds an additional terminal node for missing values which H2O-3 does not do).
max_depth = 1
max_depth = 2
max_depth = 3