Wow. You have several serious issues to deal with before trying to get the Asperger's diagnosis. Whatever is going on that has you seeking an Asperger's diagnosis must be pretty difficult to deal with. Based on your OP (original post) and your responses to the comments I think that you're having some serious communication issues with your husband and/or social interactions with others. I don't get the feeling that depression is really a factor.
The DSM-5, which is used mainly in the USA, combines Asperger's in with Autism as the Austism Spectrum Disorder (ASD). The ICD-11 also lists Asperger's as a subheading under Autism, so you're correct that a diagnosis of Asperger's will be the same as a diagnosis of Autism. Though it's become a more visible diagnosis in the US due to numerous educational campaigns it is still unfortunately seen as a disorder that mainly affects boys and men. There have been many studies in the UK over the past 15yrs that have specifically researched the differences in symptom presentation between males and females that should be much more broadly known but are not. I eventually had to strongly insist (a big argument) that my therapist actually READ some of the research that I had given her before she would test me and then actually BELIEVE that I have Asperger's. (Click
here for the best site I've found for UK research) Theony is that she spent much of undergraduate and graduate studies in research specifically dealing with Autism. She's an awesome therapist who is able to match me verbally and intellectually which prevents me from being able to manipulate her. This is important for 2 reasons, one is that I have far too much experience with psychiatric treatments having been hospitalized numerous times for extremely long times. Unfortunately this is fairly common for women with Asperger's because we are often misdiagnosed with Borderline Personality Disorder, Schizo-Affective Disorder or some other major mental health issue which is almost always combined with Major Depressive Disorder and Social Anxiety Disorder. The second reason is that I need to be able to learn how to function in society and deal with the past traumas related to being undiagnosed properly until 2yrs ago when I was 48.
All of this was to let you know that I understand what you're looking for and why. However, until you can resolve at least one of the following issues I think that you will not have much luck in getting what you are looking for, which is validation for WHY you are having the issues you are dealing with.
1. You said that you were lucky to find a therapist who does not charge you. I understand that very well. It's really hard to find therapists here in the USA that accept Medicaid. Well, actually many do but they have so many clients already that the problem is finding one who will take new clients.
2. The language barrier is a real problem. Even if all you are looking for is an unofficial diagnosis you will need to have your therapist be able to interact with you fluently so that he can establish to his own satisfaction the difficulties that you experience with social interactions. Even a therapist who is fluent in English but did not grow up in the USA will still have major difficulties because of the differences in cultural upbringing. I have always fit in better with people from other cultures because they didn't recognize my social clumsiness due to their own lack of knowledge of cultural norms here in the USA. As an aside, why haven't you simply asked your therapist where he is from and/or what his first language is?
3. Apparently your husband isn't very supportive of your attempt to get assistance in this matter. I have a feeling that he believes you are trying to use this as an excuse for the difficulties between the two of you rather than you simply accepting that you are at fault. This is simply my opinion which is based on very little information so if I'm incorrect please don't take offense. My guess is due to seeing many women who deal with husbands that don't want to acknowledge that marriage (or any relationship for that matter) is a partnership which means that you BOTH bear responsibility for the problems. It is never one person's fault but typically (not always) the woman is the one that takes the point of view that she alone is responsible.
If finding a different therapist that is at least fluent in English is not possible right now then your only option is to find a way to get your husband to be more supportive of you which would then give you the option of finding an appropriate therapist. I wish you luck and truly hope that you are able to find the support that you need.