Isaiah 53:5 –
But He was wounded for our transgressions,
He was bruised for our iniquities;
The chastisement for our peace was upon Him,
And by His stripes we are healed.

Does this last line refer to physical healing, or spiritual?

Could healing not occur before the stripes?  Yes, God healed in the old testament as well as during Jesus ministry prior to the crucifixion.

Is this intended as a promise to believers for an assurance of healing?  It does not seem to be the case – there are many Christians with physical ailments, and some of them die.  Indeed, since “old age” isn’t a legitimate medical cause of death, everyone (including those previously healed) who doesn’t die of violence will die of some physical ailment (rapture notwithstanding).

Taking the view that this is a healing promise from God is dangerous in that expectations are built up for disappointment and disillusionment if healing does not occur.  The false doctrine of the “health and wealth gospel” or “prosperity gospel” asserts that Christians should expect financial prosperity and physical health as guaranteed sign-on perks, and that if one does not possess them, then one’s faith is deficient.  This is a false view of the purposes of God; his objective is not to make us happy in this life, it is to perfect our character.  For most of us, luxury and comfort foster complacency and self-reliance; for some few others, wealth and health is properly used in selfless generosity.  When the clock runs smoothly, we often forget the clockmaker.  In The Problem of Pain, C. S. Lewis says that “Pain is God’s megaphone to rouse a deaf world.”

I will not deny that God can and does heal; I know of many cases where miraculous healing makes the best explanation.  But I think the context of the phrase in the verse, as well as the evidence of our Christian life experience seems to indicate that this is intended to mean the spiritual healing of a restored relationship with God through Christ’s sacrifice.