I am planning to undertake online-Delphi. I have quantitative questions in a binary form (yes vs. no) and also qualitative questions in a form of comments or remarks.
If I am correct - are you asking if there is single online software that can perform both quantitative and qualitative in the same programme? If so - then the answer is no. If we take a few market leaders - such as SPSS and NVivo - they use a completely different metric. For your Delphi - you would have to use NVivo for your qualitative first-round - and SPSS for subsequent likert survey statement rounds.
The following may assist - a mixed-methods chapter detailing Delphi and an earlier Delphi study of mine. Personally, I didn't feel the need to use any software. It depends how far beyond description you wish to venture.
From your question it's unclear whether you need software to collect and store the data, or software to conduct the analysis.
If it is the second, I would agree with Dean's answer - with the additional caveat that Nvivo and SPSS are not free online tools but commercial software that you need to download. Your institution may have access to these, or to similar software packages, so it is worth checking about that.
If you are wondering about software packages that can collect and store both qualitative and quantitative data, from my own experience I can recommend Google Forms: https://www.google.co.uk/forms/about/. It is free, and enables the user to design questionnaires that have both quantitative and qualitative questions. All the responses to a questionnaire can be downloaded into a spreadsheet, from which you can conduct further data processing and analysis.
All of the major Qualitative Data Analysis programs now provide options for what they call "mixed methods" data. This amounts to a rectangular data array where the rows are cases and the columns are codes, including the possibility of including pre-assigned codes such as your yes-no variables.
You can use the yes-no codes to "filter" your qualitative data, or you can export the entire data set in spreadsheet form, so that it can be read by Excel or SPSS etc. Or, going the other way, you can import spreadsheet data and add codes to those cases.
If you are limited to on-line tools, then check out Dedoose, which has a strong emphasis on combining quantitative variables with qualitative coding.
It's not online but it seems that Maxqda is working on this kind of integration. For now I think it works with survey results from Survey Monkey (both quantitative and open text questions).
I haven't tested it yet, so please let me know if you do : I'd be interested to know how it went.