Can JSA Claimant invite family?

[eleven45]

Hello,
I am british born. I have a fiancee (we will get married) and a 17 months old boy. They are both completely dependent on me.
I have had several temp jobs in the last seven months but now on JSA.

My question is this: Is there a remote possibility I can invite both of them over while on JSA?

This information might be of help:

I have a back injury and a specialist had asked in december to quit work for up to eight months until recovery. I have not acted on this.
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I have been told by the passport office that my son inherits citizenship from me since I was born before 1983.

Thank a lot. All responses will be appreciated.

Michael