I think we must start to be satisfied in the concept that 'God suffers' in some sense when we suffer, from the basic premise that he loves us. On the other hand, God can't suffer in the sense that it takes away the endless joy and boundless relaxed tranquility of the infinite pleasure he has in his perfect will, without any shadow of turning in his own joy. In other words, God is always rejoicing with infinite joy, therefore you will not find any scripture speaking about God as suffering within his own divinity. His suffering can only be another kind as an outflow of his love for us which can exists together with eternal infinite joy.
We are grappling with a mystery here so words are not quite good enough for the explanation. However, we must proceed upon something when grappling with the incarnate mystery of God in the flesh and how that has manifested his divine live for humans. So we will proceed to map it out from a scriptural standpoint without trying to fully understand it. One one hand, we know that God suffers when we suffer because love can't rest when its beloved suffers. It's a fact of god given reason. It's an essential emotional element of love that must have a spiritual equivalent in the infinite glory of God, otherwise he would not have created love to behave this way. Furthermore, Christ being the manifestation of tue divinity with his divine love possessing a human soul and body and we see that Christ also suffered when his loved ones suffered. Christ also proved that he suffers by literally suffering that we might not suffer. This clearly shows that God suffers in human terms, using human words to describe it. Although the divinity can't cry or walk around moping and mourning, being eternally joyful, we see God's empathy (the ability to suffer when others suffer) when assuming human form, having compassion on us, being 'a man of sorrows' and dying for us. It's an extrapolation of redemption through the incarnation and death of God's only son.
We might not have known that God had the attribute of empathy but as manifested in the God-Man this divine quality became more than just an abstract inference from the basic assumption in the word 'love':
For we do not have a high priest who is unable to empathize with our weaknesses, but we have one who has been tempted in every way, just as we are —yet he did not sin. (Hebrews 4:15, NIV)
Of course we see the divine empathy everywhere when we read the gospels. The way Christ speaks to individuals shows that his emotions are filled with empathy, never breaking the bruised reed, or snuffing out a smoldering wick. (Matth12:20). Even the simple fact that Christ's emotions were tender by the direct unlimited influence of the Spirit, causing his empathetic and generous soul to 'deeply feel' for those about to be judged, indicates his suffering for the suffering of others:
As he approached Jerusalem and saw the city, he wept over it. (Luke 19:41, NIV)
So although the bible does not say anywhere 'God suffers when we suffer' it must be true in a certain sense for he empathizes with us in our pain and works hard to relieve ours as a result. Even to the point of offering his only Son to greatly suffer by becoming our sin that we might be his righteousness, all to take our pain into himself, for our eternal relief. If this is not divine empathy then I do not know what it is to feel the pain of another person.