Straight up? It's a yes and a no.
Yes - your relationship can survive, for better or for worse.
In some cases, there's eventually a positive that emerges long-term after infidelity - that an affair was one of the few things dramatic and life-changing enough to bring the couple back to a strong erotic connection. It's like the reality of potentially losing everything wakes the couple up from apathy about their relationship and shows them they still want each other. But that said, it's not a risk you want to take.
More often than not, infidelity destroys a far greater part of a relationship than it leaves intact. Although cheating doesn't mean it has to end, it does mean the end of trust for an extended period of time. And trust is fundamental to good relationships. Recovering from infidelity is long, hard work and you'll only be motivated to do that hard work of rebuilding from the ground up if you both still truly value and want to be with each other. It will require some soul-searching all round and couple therapy can be a good option for doing that.
In the first stage of therapy after infidelity we tend to focus most on the person who is hurt and explore together whether there is still love and desire for healing between the partners once the smoke has cleared. The person who had the affair is also their own victim to some extent in that they too suffer trauma and loss in the aftermath of the affair. They may have lost a lover they cared about as well as their secure relationship. They may have lost clarity, faith and understanding of themselves and be feeling grief-stricken and deeply confused. Everyone involved, children too if they know about it, will be traumatised and suffering great feelings of loss for multiple reasons in the early days after an affair comes to light. However, a primary focus on the partner who was deceived and support for other family members is the first therapeutic concern. There's shock, intense grief and loss to be lived through and much support is needed.
Once life begins to re-stabilise a little, the focus of therapy can shift to understanding the reasons, the inspiration for the affair. It's often useful to focus on what the partner who had the affair was looking for, hoping for, yearning for within themselves, rather than focusing on the qualities of the third person, which is what the aggrieved partner may feel drawn to do. Often an affair is motivated by a feeling that something is missing in life, inside oneself more than in a partner. The third person may simply have been the person who was conveniently available at the time when the affairing partner was yearning desperately to feel young again or virile, or loved, rather than them being better than the long-term partner in some mysterious way. It's helpful to have full disclosure about what happened but it's equally important for the deceived partner not to torture themselves unnecessarily by asking to replay intimate details of betrayal .
It's important to work out - what needs set the partner who had the affair on fire so much that they were willing to risk everything to feel that way? Then you can both look at other potential ways to fulfill those needs in yourselves and help each other with them. What were they yearning for in themselves that they found in the other person? What have they been desperately missing in life, how long for? How else can you live a passionate, loved-up, erotic and thrilling life, if not through affairs?
Answers to these questions, if you can find them, can be deeply healing and change lives and relationships for the absolute better. They also re-cast the third person in an affair to some extent, from powerful villain to an outsider.
Infidelity is deeply destructive but not deadly. It is the end of one relationship, but it can also be the start of a new one between the same couple, given a rekindling of desire and a hell of a lot of hard work. Make sure you can handle your own inner truth, and get ready to also share it way better than before.
If you're looking for fun ideas for how to reconnect romantically in your relationship and spice things up, look no further! I've got plenty of resources, some of them free, for creating the life and relationship you most desire.