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Using an OR function/operator in a COUNTIFS?

Is it at all possible to include an OR function or alternation as part of the criterion of a COUNTIFS function, and if so, how is it done?

I want to count the number of times an entry/row within a certain date range, and with one of two specific text values, appears in a given table. I did try using SUMPRODUCT instead, but couldn't get it to cooperate and it was harder to read. Currently the formula that I'm using to give me the number I want is:


I would prefer something along the lines of:


But nothing I input seems to work. The wiki states that COUNTIFS takes regular expressions, and "Web*" will return a count for all entries with "Website" just fine, but for some reason the | regex operator doesn't work. (||, and "Website|Email" without brackets also don't work.) I also can't use OR() since there doesn't appear to be any way to reference the COUNTIFS criteria within the criterion (attempting OR(H14="Website",H14="Email") doesn't appear to work at all; even when H14 does contain either "Website" or "Email", the resulting count is 0).

The example I've used may look pretty minor as a use case, but I'm going to be SUMing several more of these together across sheets and would prefer to eliminate the need to double up on functions.