I would like to know what "said through a bite of radish" means in the following sentences:
‘So you’re students,’ the mother said.
‘Yes, ma’am,’ you said through a bite of radish, looking more at ease than I felt. ‘Just finished our studies.’
She nodded, as if she was agreeing to something uncertain. ‘Married?’ she asked, looking at you.
‘No, ma’am,’ you said, shaking your head, smiling at her. ‘Not yet. Am still young.’
She laughed in her hoarse voice, revealing a set of missing front teeth.
In this novel which is set in the 1980's in Poland under the socialist regime, where homosexuality was socially unacceptable, the protagonist Ludwik (a university graduate) left Poland in 1981 to live in the United States of America. And he remembers what it was like back then in Poland, where he went to the agricultural camp (which was mandatory for college graduation). At the camp, he met Janusz, who would soon become his lover. After the camp, Ludwik decided to go to a lake district with Janusz. On the way to the lake district, it rained through the night and they decided to stay the night at a barn of some family living at a farmhouse. In the morning, after their night stay, they were invited to the family's kitchen for breakfast. At the table, the wife of the farmer asked Janusz some questions.
In this part, I wonder what "saying through a bite of radish" means. Would that mean he took a bite, swallowed, said, and took another bite? Or would that mean he took a bite and said, the radish still in his mouth?
I am an English learner from South Korea, so thank you for your patience in advance as I may not know obvious things. I would very much appreciate your help. :)