COUNTIFSVISIBLE

Returns the number of visible non blank cells that satisfies multiple conditions.

'rgeCountRange - 
'avCriteriaAndRanges - 

Public Function COUNT_IFSVISIBLE(ByVal rgeCountRange As Range, _ 
                                 ParamArray avCriteriaAndRanges() As Variant) As Single 
                                
Dim avCriterias() As Range 
Dim asCriterias() As String 
Dim icriteriacount As Integer 
Dim rgeCriteria As Range 
Dim sCriteria As String 
Dim iitemcount As Integer 
Dim lrowno As Long 
Dim lmatch As Long 
Dim arsngvalues() As Single 
Dim sngmedian As Single 
Dim bsorted As Boolean 
Dim vcell As Range 
Dim vcellvalue As Variant 

   If UBound(avCriteriaAndRanges, 1) Mod 2 > 0 Then 
      'not the correct amount of arguments
   End If 
   
   ReDim avCriterias(1 To UBound(avCriteriaAndRanges, 1)) 
   ReDim asCriterias(1 To UBound(avCriteriaAndRanges, 1)) 
   icriteriacount = 1 
   
   For iitemcount = 0 To UBound(avCriteriaAndRanges, 1) Step 2 
      If TypeName(avCriteriaAndRanges(iitemcount)) = "Range" Then 
         Set rgeCriteria = avCriteriaAndRanges(iitemcount) 
      End If 
      If TypeName(avCriteriaAndRanges(iitemcount + 1)) = "String" Then 
         sCriteria = CStr(avCriteriaAndRanges(iitemcount + 1)) 
      End If 
      
      Set avCriterias(icriteriacount) = rgeCriteria 
      asCriterias(icriteriacount) = sCriteria 
      icriteriacount = icriteriacount + 1 
   Next iitemcount 

   For lrowno = 1 To rgeCriteria.Rows.Count 
      Set vcell = rgeCriteria.Parent.Cells(rgeCriteria.Row + lrowno - 1, rgeCountRange.Column) 
      vcellvalue = rgeCriteria.Parent.Cells(rgeCriteria.Row + lrowno - 1, rgeCountRange.Column).Value 
      
      If Row_MatchesAllCriteria(lrowno, avCriterias, asCriterias) = True And _ 
         vcell.EntireRow.Hidden = False Then 
         lmatch = lmatch + 1 
      End If 

      If lmatch > 0 And IsEmpty(vcellvalue) = True Then Exit For 
   Next lrowno 

   COUNT_IFSVISIBLE = lmatch 

End Function 

Public Function Row_MatchesAllCriteria(ByVal lrowno As Long, _ 
                                       ByVal vArrayCriteria As Variant, _ 
                                       ByVal sArrayCriteria As Variant) As Boolean 

Dim avCriterias() As Range 
Dim asCriterias() As String 
Dim rgeCriteria As Range 
Dim sCriteria As String 

Dim iitemcount As Integer 
Dim bmatch As Boolean 
Dim iconditioncolno As Integer 
Dim icriteriacount As Integer 

   ReDim avCriterias(UBound(vArrayCriteria, 1)) 
   ReDim asCriterias(UBound(sArrayCriteria, 1)) 

   For iitemcount = 1 To UBound(vArrayCriteria, 1) 
      If TypeName(vArrayCriteria(iitemcount)) = "Range" Then 
         Set rgeCriteria = vArrayCriteria(iitemcount) 
      End If 
      If TypeName(sArrayCriteria(iitemcount)) = "String" Then 
         sCriteria = CStr(sArrayCriteria(iitemcount)) 
      End If 

      Set avCriterias(iitemcount) = rgeCriteria 
      asCriterias(iitemcount) = sCriteria 
   Next iitemcount 

   bmatch = True 
   For icriteriacount = 1 To UBound(avCriterias, 1) 
      iconditioncolno = avCriterias(icriteriacount).Column 
      If avCriterias(icriteriacount).Parent.Cells(avCriterias(icriteriacount).Row + lrowno - 1, iconditioncolno).Value = _ 
                                                  asCriterias(icriteriacount) Then 
      Else 
         bmatch = False 
      End If 
        
   Next icriteriacount 
        
   Row_MatchesAllCriteria = bmatch 
End Function 

Alternatives

You can use SUBTOTAL with 103 to achieve this
You can use AGGREGATE with 3 to achieve this