Are filtered COUNTIFS possible?

OK so, to count how many rows are nonblank in both of two columns, I am using this formula: =COUNTIFS(BFQ4:BFQ4595,"<>",BFU4:BFU4595,"<>").
But, how do I make this exact function work for filtered ranges only?

Thanks!

Are you really using 1,529 columns (A to BFU)?

The simplest way to handle this sort of thing uses an additional column, say BFV or even further right. I'll assume BFV is available.

BFV4:

Formula:

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filled down into BFV5:BFV4595. These evaluate nonzero when some cell on the same row in columns A to BFU contain something AND are visible with respect to filters.

Formula:

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should then return the count of rows visible after filtering in which columns BFQ and BFU are both not blank.