Entering into Trust Deeds will not affect your partner or spouse unless you have joint debt together.
When you sign a credit agreement, because you have done so in your own name; your spouse or partner is not responsible to pay your debts. If you start a Trust Deed, your partner or spouse will not be directly involved with the agreement.
They will not be forced to help you repay your debt and your creditors are forbidden from revealing details of the debt to your partner/spouse unless given clear permission to do so by you.